Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

<image>

In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in JAVA):

Solution:
import java.util.*;

public class q3
{
	public static void main (String[] args) throws java.lang.Exception
	{
		Scanner sc = new Scanner(System.in);
		int h = sc.nextInt();
		int w = sc.nextInt();
		int [][] g = new int[h][w];
		int [] rmin = new int[h];
		int [] cmin = new int[w];
		int min = 501,sum = 0,rsum = 0,csum = 0;
		if(h<=w){
		for(int i = 0;i<h;i++){
			min = 501;
			for(int j = 0;j<w;j++){
				g[i][j] = sc.nextInt();
				sum+=g[i][j];
				if(g[i][j] < min){
					min=g[i][j];
					}
			}
			rmin[i] = min;
			rsum+=rmin[i];
		}
		for(int i = 0;i<h;i++){
			if(rmin[i]!=0){
			for(int j = 0;j<w;j++){
				g[i][j] -= rmin[i];
			}
			}
		}
		
		for(int i = 0;i<w;i++){
			min = 501;
			for(int j = 0;j<h;j++){
				if(g[j][i] < min){
					min=g[j][i];
					}
			}
			cmin[i] = min;
			csum+=cmin[i];
		}
		int ans = csum+rsum;
		if(((csum*h)+(rsum*w))!=sum){
			System.out.println(-1);
		}
		else{
			System.out.println(ans);
		for(int i = 0;i<h;i++){
			if(rmin[i]!=0){
			for(int j = 0;j<rmin[i];j++){
			System.out.println("row "+(i+1));
			}
			}
		}
		for(int i = 0;i<w;i++){
			if(cmin[i]!=0){
			for(int j = 0;j<cmin[i];j++){
			System.out.println("col "+(i+1));
			}
			}
		}
		}
		}else{
		for(int i = 0;i<h;i++){
			for(int j = 0;j<w;j++){
				g[i][j] = sc.nextInt();
				sum+=g[i][j];
			}
		}
		for(int i = 0;i<w;i++){
			min = 501;
			for(int j = 0;j<h;j++){
				if(g[j][i] < min){
				min = g[j][i];
				}
			}
			cmin[i] = min;
			csum+=cmin[i];
		}
		for(int i = 0;i<w;i++){
			if(cmin[i]!=0){
			for(int j = 0;j<h;j++){
				g[j][i] -= cmin[i];
			}
			}
		}
		
		for(int i = 0;i<h;i++){
			min = 501;
			for(int j = 0;j<w;j++){
				if(g[i][j] < min){
					min=g[i][j];
					}
			}
			rmin[i] = min;
			rsum+=rmin[i];
		}
		int ans = csum+rsum;
		if(((csum*h)+(rsum*w))!=sum){
			System.out.println(-1);
		}
		else{
			System.out.println(ans);
		
		for(int i = 0;i<w;i++){
			if(cmin[i]!=0){
			for(int j = 0;j<cmin[i];j++){
			System.out.println("col "+(i+1));
			}
			}
		}
		for(int i = 0;i<h;i++){
			if(rmin[i]!=0){
			for(int j = 0;j<rmin[i];j++){
			System.out.println("row "+(i+1));
			}
			}
		}
		}	
		}
	}
}